Randall V. Tarr*
and Paul G. Steffes
School of Electrical and Computer Engineering Georgia Institute of Technology
Atlanta, GA 30332-0250
* Current address: Siemens Medical Systems Incorporated 4040 Nelson Avenue
Concord, CA 94520
The efficacy of home blood glucose monitoring in the treatment and maintenance of insulin dependent diabetic patients is well established [1,2]. However, the necessity of drawing capillary blood for each sample, and well as the time and cost required for each measurement limits the frequency of such measurements to 5-10 per day, even for highly motivated patients. The increasing availability of insulin infusion pumps, combined with the availability of fast-acting insulin analogs, such as lispro, strongly motivates development of sensors, either implantable or non-invasive, providing frequent or continuous blood glucose measurement, which would be useful in patient-based blood glucose control, or in a closed-loop automated insulin delivery system. Due to the enormous potential benefits of tight blood glucose control in diabetic patients, many different techniques have been tried in an attempt to non-invasively measure blood glucose concentration. The common thread among nearly all non-invasive techniques is the use of electromagnetic radiation to measure directly, or to infer indirectly, the blood glucose concentration. The system developed at Georgia Tech  uses stimulated Raman spectroscopy to measure glucose concentration in the aqueous ocular humor, so as to indirectly infer blood glucose concentration.
Although many attempts at non-invasive glucose measurement have directed electromagnetic radiation through the skin to measure blood glucose directly, the aqueous ocular humor provides a more promising point of measurement. The blood is a very difficult medium in which to spectroscopically measure very small concentrations of minor constituents such as glucose, principally because of the spectral dominance of the hemoglobin. Additionally, variations in skin transmissivity can be problematic. The ocular aqueous humor is a spectroscopically simpler medium, since there are fewer molecular species present which might interfere with the measurement of glucose concentration, and the cornea is essentially transparent to both near-infrared and visible wavelengths. Direct chemical analysis has shown that the glucose concentration in the ocular aqueous humor is proportional to the blood glucose concentration and tracks variations in blood glucose concentration quite promptly , so that blood glucose concentration can be inferred from the measurement of the glucose concentration in the aqueous humor.
III. USE OF STIMULATED RAMAN SPECTROSCOPY
March et al. [5,6] proposed two different approaches for the measurement of glucose in the ocular aqueous humor involving measurement of effects of glucose on refractive index and measurement of the polarization effects, or optical activity, of the glucose present in the aqueous humor. Unfortunately, other refractive and optically active compounds in the aqueous humor made it nearly impossible to unambiguously measure glucose concentration in these ways [7,8]. An alternative approach is to use stimulated Raman spectroscopy for measurement of glucose in the ocular aqueous humor. As in most forms of spectroscopy, the Raman spectrum of glucose makes it spectrally differentiable from other constituents. (See Figure 1.) The use of stimulated Raman spectroscopy makes possible detection of a single predominant feature in the Raman spectrum using relatively low-cost fixed wavelength lasers. Additional benefits include increased resistance to interference from luminescence and florescence, and resolution which is limited only by the laser linewidths. (See, e.g., .) Sensing of ocular glucose is accomplished by combining the two laser wavelengths and then passing them tangentially through the front of the eye. (See Figure 2.) A detection system then measures the amount of power translated from one wavelength to the other, which is related to glucose concentration.
For stimulated Raman gain spectroscopy, the Raman-active medium is excited with a pump and a probe laser whose frequencies are separated by a Stokes shift of the Raman-active medium. In this case, the stimulated Raman effect essentially converts a portion of the pump laser power to the proble laser wavelength. The stimulated Raman effect requires no phase matching between the two laser beams, only that they be spatially overlapping in the Raman-active medium . When the frequency difference of the two lasers equals the vibrational frequency of the Raman-active mode, a non-linear optical interaction occurs between the optical field and the medium. The strength of the nonlinear optical interaction depends upon the third order nonlinear susceptibility, c(ws), of the medium. The result of this interaction is a coherent increase in the irradiance of the Stokes (probe) beam and a corresponding decrease in the irradiance of the pump beam.
A semiclassical model can be used to determine the gain, gs, of the Stokes beam in which the electromagnetic fields are treated classically, and the medium is treated guantum mechanically . Consider the specific case of stimulated Raman gain spectroscopy, in which the pump wave is at frequency wp and the Stokes wave is at frequency ws The growth of the Stokes wave is governed by
where ns is the refractive index at the Stokes wavelength. Assuming plane wave solutions to the wave equation, the electric field at the Stokes frequency, ws is
where is a vector constant and ks is the propagation constant. It has been determined that for isotropic media, such as liquids, there are only 21 non-zero elements in the third order susceptibility tensor and only three of these are independent . For a liquid medium illuminated by two spatially overlapping fields with parallel polarization of the vector fields, the susceptibility tensor reduces to a scalar quantity [121. Thus the third order polarization of the medium at the Stokes frequency, , is
where Ep represents the vector field at the pump frequency wp, Es represents the Stokes field at frequency ws and c(3)(ws) is the third order susceptibility constant of the medium. Substituting for Es & Ps, in equation (1) and time averaging gives
Solving for the propagation constant, ks,
where is the pump laser irradiance. Using the binomial theorem leads to the approximate relation
In the vicinity of a resonance the susceptibility can be broken down into its component parts, is the real part of the resonant contribution, is the imaginary part of
the resonant contribution, and cNR is a term accounting for the nonresonant background . Using this relation for and defining the expression for ks, can be separated into its real and imaginary parts
Now this expression for ks, can be substituted back into equation (2) to yield
Now the irradiance of the Stokes field, Is(z), is of the form
where Is(0) is the initial irradiance of the Stokes wave and the stimulated Raman gain, gs, is given by
From a quantum mechanical treatment of a liquid medium, the imaginary part of the third order susceptibility constant can be expressed in terms of the spontaneous Raman scattering cross section, and the Raman transition line width G as 
where D is the difference in probability of occupation of two vibrational levels, N is the density of molecules, and hmks is Plancks constant in mks units. Substituting into the expression for the stimulated Raman gain yields
and at the resonance peak wp-ws=w0 which leads to a peak stimulated Raman gain of
Unfortunately, no measurement of the nonlinear susceptibility of D-glucose has been reported. However, an estimate of the imaginary part of the third order susceptibility for D-glucose may be obtained from the spontaneous Raman spectra of a 30% D-glucose solution shown in Figure 1. From Equation (11) the imaginary part of the third order susceptibility may be determined from the spontaneous Raman cross section, , and the linewidth, G for the 518 cm-1 resonance of D-glucose. The spontaneous Raman cross section for the 518 cm-1 resonance can be estimated from the spontaneous Raman cross section of the 3655 cm-1 resonance of water which has been measured to be (9±2) x 10-30 CM2/sr.mol . From Figure 1 it is evident that the linewidths of these two resonance peaks differ. To account for this difference between the linewidths of these two resonance peaks, the peak Raman scattering cross section for each resonance is determined. Assuming a Lorentzian shape for each Raman line, the peak Raman scattering cross section, can be related to the spontaneous (integrated) Raman cross section by .
where G is the resonance linewidth in Hertz. By fitting a Lorentzian line shape to the 3655 cm-1 resonance of water, the linewidth in wavenumbers, is found to be approximately 200 cm-1 and the corresponding peak Raman scattering cross section, is 3 x 10-32 cm3/sr.mol. from Equation (14). From the spontaneous Raman spectrum for the D-glucose solution-shown in Figure 1, the peak Raman scattering cross section for the 518 cm-1 resonance of D-glucose is
Abundance normalization of the peak Raman cross section yields
The linewidth of an equivalent Lorentzian line which has been fit to the 518 cm-1 resonance Raman cross section for the 518 cm-1 resonance of D-glucose is calculated to be
The imaginary part of the third order susceptibility for the 518 cm-1 resonance of D-glucose may be estimated by using the calculated value for the spontaneous Raman scattering cross section and the linewidth with Equation (11). Specifically, substituting the following values:
and the value for the Raman scattering cross section into Equation (11) yields a value for the imaginary part of the third order susceptibility for D-glucose, of
Figure 3 shows the stimulated Raman signal gain vs. the D-glucose concentration with various laser beam diameters. These gain curves have been calculated using Equation (10) with a pump laser power of 10mW and a Stokes wavelength of .85 mm. The smallest D-glucose concentration used in these calculations, h=.0001, is smaller than the minimum D-glucose concentration present in the ocular aqueous humor [6, 7]. The optical power level of 10mW is approximately equal to the optical power levels used in our hardware implementation shown in Figure 4. Values on the gain curves can be related to a stimulated Raman signal amplitude by
where z@1 cm in the ocular aqueous humor . Upon substitution of the appropriate values for D-glucose into Equation (13), we have
where h is the glucose concentration and r represents the laser beam radius in centimeters. From these gain curves it is evident that a very small beam diameter is necessary to produce stimulated Raman signal levels which are measurable in the presence of noise. The noise level is determined by the amplitude noise present on the probe laser and by the shot noise produced during photodetection.
D. Plane Wave Propagation through the Ocular Aqueous Humor
In order to determine an optical path laterally through the ocular aqueous humor, a plane wave analysis has been performed. The eye is approximated by a sphere with a radius of curvature, r =7.42mm, comparable to that of the cornea. The optical beam is approximated by a cylindrically symmetric array (a bundle) of filament rays (plane waves). This constructions allows the intensity to vary across the wavefront and the curvature of the dielectric interface to be modeled. The optical path length through the sphere is constrained to be ~1 cm which is comparable to that of the ocular aqueous human . Figure 5 illustrates the path through the sphere by a filament ray at the center of the bundle.
A computer model has been constructed to simulate plane wave propagation through the ocular aqueous humor. The program traces multiple filament rays which comprise an optical beam through a sphere with a radius of curvature equal to 7.42 mm  which approximates the curvature of the cornea. Figure 6 shows a cross section of the optical beam which illustrates the quantization of an optical beam into multiple filament rays. The initial power distribution among the filaments within the beam can be adjusted to model various intensity profiles, such as Gaussian. Several simulations have been performed with different beam diameters and initial intensity profiles. Table 1 gives the initial power distributions among the filaments for both a uniform intensity profile and a Gaussian intensity profile. During the computer simulation the optical power levels are monitored in the regions shown in Figure 7. From these simulations it is evident that even though a collimated beam is incident upon the sphere, the optical beam is focused to a point within the sphere before exiting on the opposite side. This focusing effect is useful since the simulated Raman signal is directly related to the irradiance of the optical beam within the Raman-active medium. From Table 2 a comparison of the optical power levels in the defined regions may be made for various optical beam diameters and initial intensity profiles.
E. Laser Power Constraints
The total laser power used in this implementation of the stimulated Raman effect is limited by the maximum permissible exposure to the eye. The energy in the near-infrared wavelength band is highly absorbed by the retina, but not by other structures within the eye . Table 3 gives the maximum permissible exposures for direct intrabeam viewing with various exposure times, specifically for optical power at 800 nm wavelength. From the analysis in the previous section with 15 mW incident power approximately 3 mW remains in the sphere. For exposure times greater than ~0.3 sec, this energy exceeds the maximum permissible exposure levels in Table 3. However, from the geometry of the opttical system, the optical power which remains within the aqueous humor does not reach the retina since it is blocked by the iris. Therefore, it may be permissible to safely exceed the established standards for the maximum permissible exposure without ocular damage.
Two test systems were developed to demonstrate the feasibility of this measurement approach. The first was a fiber-optics based system wherein both the filtering and combining system for the laser beams from the two solid-state laser sources, and the detector system, were constructed from relatively low-cost fiber optic components, with the test cell, representing the eye, being the only region of unguided wave propagation. The second system was a free space optical system, which provided better isolation between the pump and probe wavelengths in the detection system and avoided any spurious Raman activity in the fibers. (See Figure 4.) With relatively low power solid-state lasers, (probe power: 50 mW pump power: 100 mW) it has been possible to detect a 0.5% concentration of glucose over a 10 cm long path in an aqueous solution. (See figure 8.) Since the sensitivity of such systems is related to the power and stability of the lasers used, in addition to the spatial compactness of the beams, the use of higher stability, higher power semiconductor lasers with more compact and uniform spatial beamwidths should make possible measurement at the 0.01% level or better over paths of less than 1 cm.
A technique has been devised to non-invasively measure the D-glucose concentration in the ocular aqueous humor. This approach is radically different from conventional invasive blood glucose measurement techniques. A major benefit of this technique is that no wavelength tuning is required, which allows the use of economical fixed wavelength semiconductor lasers. Using the limited resources available, this concept has been experimentally demonstrated by the construction and evaluation of two independent in-vitro measurement systems. However, the sensitivity of the experimental systems must be improved in order to measure the extremely small D-glucose concentrations present in the aqueous humor. In addition, theoretical studies have been performed to determine the feasibility of the stimulated Raman spectroscopy technique for in-vivo measurements in the ocular aqueous humor. The results from these theoretical studies indicate that the stimulated Raman signal amplitude levels produced from the very low D-Glucose concentrations present in the aqueous humor should be detectable using solid-state electro-optical components.
 Ross, D., Self glucose monitoring, The Alabama Journal of Medical Sciences, vol. 20, pp. 441-449, April 1983.
 Chase, H., Monitoring glucose contol and use of a diabetes control index in insulin dependent diabetes mellitus, Pediatric Annals, vol.12, pp. 643-650, September 1983.
 Tarr, R.V. and P.G. Steffes, Non-invasive blood glucose measurement system and method using stimulated Raman spectroscopy, United States Patent #5,243,983 - September 14, 1993.
 Prince, J., The Rabbit in Eye Research, C.C. Thomas Publishers, Springfield, IL 1964.
 March, W. Non-invasive automatic glucose sensor system, United States Patent #3,958,560 - 1976.
 Rabinovich, B., W. March, and R. Adams, Noninvasive glucose monitoring of the aqueous humor of the eye: Part I. Measurements of very small optical rotations, Diabetes Care, vol. 5, pp. 254-258, May-June 1982.
 Rabinovich, B., W. March, and R. Adams, Noninvasive glucose monitoring of the aqueous humor of the eye: Part II. Animal studies and the scleral lens, Diabetes Care, vol. 5, pp. 259-265, May-June 1982.
 Gough, D., The composition and optical rotary dispersion of bovine aqueous humor, Diabetes Care, vol. 5, pp. 266-270, May-June 1982.
 Owyoung, A. and E. Jones, Stimulated Raman spectroscopy using low-power cw lasers, Optics Letters, vol. 1, pp. 152-154, November 1977.
 Pantell, R. and H. Puthoff, Fundametnals of Quantum Electronics, Wiley, New York, 1969.
 Harper, P. and B. Wherrett, Nonlinear Optics, Academic Press, New York, 1977.
 Harvey, A., Chemical Applications of Nonlinear Raman Spectroscopy, Academic Press, New York, 1981.
 Maier, M., W. Kaiser, and J. Giordmaine, Backward stimulated Raman scattering, Physical Review, vol. 177, pp. 580-599, January 1969.
 Wolff, E., Anatomy of the Eye and Orbit, 6th edition, W.B. Saunders Co., 1969,
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